The government is facing increased scrutiny of various aspects of its response, from ordering social distancing measures weeks later than European neighbours to its provision of safety equipment to frontline health workers.
"There's a pattern emerging here: we were slow into lockdown, slow on testing, slow on protective equipment," Starmer said, as he also questioned Britain's sluggish testing regime.
Foreign Secretary Dominic Raab, who is deputising for Prime Minister Boris Johnson as he recovers after being hospitalised for COVID-19, insisted ministers had been guided by scientific and medical advisers "at every step along this way".
"I don't accept his premise that we've been slow," he said. "If he thinks he knows better than they do, with the benefit of hindsight, then that's his decision. But that is not the way we've proceeded."
Britain is one of the countries worst hit by the pandemic, with 18,100 deaths in hospital alone - and many more feared in care homes and the community.
The government ordered a national lockdown on March 23, but has seen mounting criticism about the extent of screening for the virus and for refusing to detail an exit strategy from the social distancing regime.
Ministers have also become embroiled in a simmering row about Britain's delay in joining an EU scheme to bulk buy medical equipment, and whether it was linked to Brexit.
The government says the delay was due to "communication problems" - but the foreign ministry's top civil servant on Tuesday said it was a "political decision".
In an extraordinary U-turn, Simon McDonald then retracted his evidence to the foreign affairs committee, writing to tell them it was "incorrect".
On Tuesday evening, Health Secretary Matt Hancock revealed that he had now agreed to join the EU scheme on an "associate" basis, but said it had yet to deliver anything.
Britain left the EU on January 31, but both sides agreed a transition until the end of the year in which relations remain largely the same. In a move that could potentially help ease some of the pressure, a Royal Air Force plane landed in Britain from Turkey on Wednesday after being sent to collect a shipment of equipment, including 400,000 badly-needed surgical gowns.
Meanwhile, Matt Hancock on Wednesday doubled down on a target to test 100,000 people daily by the end of next week.